Various interactions between the inclusion and the solidification front of the steel and the critical velocity for the entrapment of inclusions at the solidification front were summarized. Mathematical models on the fluid flow, heat transfer and solidification of the steel as well as the motion, removal and entrapment of inclusions during the continuous casting of steel were discussed. The three-dimensional spatial distribution of the number density, size, and composition of inclusions on the cross section of the continuous casting billet and slab was predicted.